`\qquad 4x^2+1`
`-> \text{Sửa đề}: 4x^4+1`
`=(4x^4+4x^2+1)-4x^2`
`=(2x^2+1)^2-(2x)^2`
`=(2x^2-2x+1)(2x^2+2x+1)`
--------------------
`\qquad 3(x^4+x^2+1)-(x^2+x+1)^2`
`=3(x^4-x+x^2+x+1)-(x^2+x+1)^2`
`=3[x(x^3-1)+x^2+x+1]-(x^2+x+1)^2`
`=3[x(x-1)(x^2+x+1)+(x^2+x+1)]-(x^2+x+1)^2`
`=3(x^2+x+1)[x(x-1)+1]-(x^2+x+1)^2`
`=3(x^2+x+1)(x^2-x+1)-(x^2+x+1)^2`
`=(x^2+x+1)[3(x^2-x+1)-(x^2+x+1)]`
`=(x^2+x+1)(3x^2-3x+3-x^2-x-1)`
`=(x^2+x+1)(2x^2-4x+2)`
`=2(x^2+x+1)(x^2-2x+1)`
`=2(x^2+x+1)(x-1)^2`
-----------------------------------
`\qquad x^5+x^4+1`
`=x^5-x^2+x^4-x+x^2+x+1`
`=x^2(x^3-1)+x(x^3-1)+(x^2+x+1)`
`=x^2(x-1)(x^2+x+1)+x(x-1)(x^2+x+1)+(x^2+x+1)`
`=(x^2+x+1)[x^2(x-1)+x(x-1)+1]`
`=(x^2+x+1)(x^3-x^2+x^2-x+1)`
`=(x^2+x+1)(x^3-x+1)`
